solve the following inequalities and write the final answer in interval notation.for unions use lower case u eg.(1,3)u(9,10)
1. 5x-12<13 and 3x+6<12=
5x-12<13 and 3x+6<12
5x < 26 and 3x < 6
x < 26/5 AND x < 2
visualize the above on a number line and draw your conclusion
I get (13+12=25)
x < 5 AND x < 2
...
To solve the inequalities, we will start by solving each inequality separately and then combine the solutions using interval notation.
1. 5x - 12 < 13:
Add 12 to both sides:
5x - 12 + 12 < 13 + 12
5x < 25
Divide both sides by 5:
(5x) / 5 < 25 / 5
x < 5
2. 3x + 6 < 12:
Subtract 6 from both sides:
3x + 6 - 6 < 12 - 6
3x < 6
Divide both sides by 3:
(3x) / 3 < 6 / 3
x < 2
Now that we have solved both inequalities, we can combine the solutions using interval notation.
For the first inequality, x < 5, the solution interval is (-∞, 5).
For the second inequality, x < 2, the solution interval is (-∞, 2).
Finally, we combine the solution intervals using union notation:
(-∞, 5) u (-∞, 2) => (-∞, 2)